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3 years ago

8

Point G is the centroid of the right △ABC with hypotenuse AB=18 in. Find CG.

1 answer:

Rama09 [41]3 years ago

5 0

<h3>Answer:</h3>

6 in

<h3>Explanation:</h3>

Let M be the midpoint of AB. ∆CMB and ∆CMA are both isosceles triangles, so CM = (AB)/2 = 9 in.

CG = (2/3)(CM) = (2/3)(9 in)

CG = 6 in

_____

<em>Comment on centroid and median</em>

The centroid of a triangle is located 1/3 the distance from the midpoint of a side to the opposite vertex. This is true for any median in any triangle. The proof can be developed from the fact that every median divides the triangle's area in half. Here, we just take advantage of this fact.

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Answer:

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Step-by-step explanation:

It is given that the money Seth withdraws was compounded every quarter for 35 years. So, we get,

Amount withdrawn every quarter, P = $4567

Rate of interest, r = $\frac{0.0101}{4}$ = 0.002525

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Now, as we know the formula for annuity as,

$P=\frac{r \times PV}{1-(1+r)^{-n}}$

where P = installments, PV = present value, r = rate of interest and n = time period.

This gives, $PV=\frac{P \times [1-(1+r)^{-n}]}{r}$

i.e. $PV=\frac{4567 \times [1-(1+0.002525)^{-140}]}{0.002525}$

i.e. $PV=\frac{4567 \times [1-(1.002525)^{-140}]}{0.002525}$

i.e. $PV=\frac{4567 \times [1-0.7021]}{0.002525}$

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i.e. $PV=\frac{1358.68}{0.002525}$

i.e. $PV=538,091.08$

So, the closest answer to initial value of the account is $538,021.66

Hence, option C is correct.

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Start by pulling out a three
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